Cycle Labelings and Eccentric Base Invariants of Graphs

Abstract

A simple graph G admits an H-covering if each edge in E(G) is a member of a sub graph of G isomorphic to H. An H-magic labeling λ of a graph G possessing an H-covering is a bijective function from the vertex-set and the edge-set of the graph Gonto the set {1,2,...,|V(G)|+|E(G)|} with a property that for every subgraph H of G isomorphic to H, the sum wtλ(H) = ∑ v∈V(H) λ(v)+ ∑ e∈E(H) λ(e) is equal to µ. The sum wtλ(H) is termed as, the H-weight. A graph is called H-supermagic if it possesses an H-supermagic labeling. Let G be a graph and v be a vertex of G. The eccentricity of the vertex v is the maximum distance from v to any vertex. That is, e(v) = max{d(v,w) : w ∈V(G)}. Firstly, we find the C4-supermagic labelings for the disjoint union of non-isomorphic copies of ladder graph, which are the generalization of the result proved in [21]. Moreover, we find the newclasses of 2-self centered graph namely uniform subdivided complete bipartite Kk n,m graph and line graph of uniform subdivided complete bipar tite graph L(Kk n,m). We also find their distance base topological indices of Kk n,m and L(Kk n,m). Then we also find eccentricity of uniform subdivided wheel graph, line graph of uniform subdivided wheel graph and their distance based topological indices